System and method for strategic budgeting of initial response for managing wildfires

ABSTRACT

The present invention provides a system and method for strategic budgeting of initial response for managing wildfires. According to the present invention, stochastic-integer-programming-based constrained optimization techniques are employed to develop a strategic budget by optimally allocating disaster management resources to disaster events belonging to scenarios associated with occurrence probabilities. According to the invention, certain machine-readable data describing fires may be subjected to computerized data processing, ultimately producing a determination of valid disaster management resources for each fire event, which may be used for strategic budgeting of initial responses for managing wildfires.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to computer-implemented stochasticoptimization modeling, and more particularly, to the use of computerimplemented stochastic optimization modeling to solve problems arisingin connection with budgeting initial responses for managing wildfires.

2. Background Description

An enterprise charged with the management of wildfires typicallyconfronts multiple scenarios corresponding to representative wild-landfires occurring in different fire planning seasons. Each such scenariois contingent in the sense that wildfire managers are unable to predictwildfires.

Prior art solutions have involved running a large number of simulationsof annual fire season scenarios and evaluating (using a predetermineddeployment plan) a candidate resource organization against the samples.Such approaches suffer from two types of problems. First, the solutionquality is tied to the choice of the initial candidate solution. Inaddition, the deployment plan does not optimize the use of availableresources in the candidate organization. Thus, neither the selection northe evaluation of the resource organization is guided by the choice ofthe optimization objective, and hence, any budget developed using suchapproaches is anything but strategic. As a result, prior art solutionsare not fully satisfactory.

SUMMARY OF THE INVENTION

Stochastic optimization refers to the minimization or maximization of afunction in the presence of randomness. Stochastic optimization modelinghas been recognized as an effective nonlinear optimization tool forvarious applications, including the solution of operations research andmanagerial problems. Stochastic optimization modeling has not previouslybeen applied to the strategic budgeting of initial responses formanaging wildfires.

An exemplary object of the present invention is to provide a system andmethod for using computer-implemented stochastic optimization modelingto solve problems arising in connection with budgeting initial responsesfor managing wildfires.

The present invention addresses shortcomings of prior art solutions byemploying stochastic optimization modeling tools to analyze complex firemanagement scenarios very quickly with fewer computational resources inorder to provide optimal strategic budgeting decisions. The presentinvention thus formulates the problem of analyzing complex firemanagement scenarios as a two-stage stochastic optimization model whichmay be solved using a two-phase decomposition approach.

According to the present invention, each scenario includes a set ofrepresentative fires, which are grouped together into blocks of firegroups to indicate their simultaneous occurrence. Due to the constraintthat each resource can be assigned to only one of the simultaneousfires, there is competition among simultaneous fires for availableresources.

Each representative fire differs in its intensity or flamelength/burning index, thereby reflecting differences in difficulty ofsuppression. Fire suppression resources (such as crew, engine, airtanker, helicopter, etc.) extinguish the fires by constructing firelines around the perimeter of the fire. Successful containment of a fireis achieved if the fire line constructed by the set of resources meetsthe perimeter of the fire at any time period (time period/containmentperiod refers to the initial attack period, i.e., the first 18 hoursafter the fire has been detected).

The number of simultaneous fires for a single group, in a reasonabledata instance, can be greater than 30, with more than 1,500 resourcesitems available for deployment over eight time periods, resulting in 400k+0/1 variables. The problem is further compounded by the fact thatthere can be 100-500 fire groups in each scenario, with varying numberof simultaneous fires.

The present invention thus provides a method and a system employingstochastic-integer-programming-based constrained optimization technologyto develop strategic budgets for allocation of disaster managementresources to disaster events belonging to scenarios, which may includefuture scenarios, associated with occurrence probabilities. Said methodand system employ as input, in a machine-readable data format:

-   -   A list of fire scenarios with unique IDs for each fire planning        unit, and their occurrence probabilities;    -   A list of fire-groups with unique IDs including simultaneous        fires in each scenario for the fire planning unit;    -   A list of fire events with unique IDs in each fire-group by fire        management unit location, fire intensity level, and sensitivity        time period;    -   A list of fire events by their respective weights (relative        utility in the utility function), burned area cumulative        perimeter growth by time period, and burned area cumulative        acres growth by time period;    -   A list of fire events with valid list of fire-management        resources;    -   A list of fire-management resources by kind, category and type;    -   A list of fire-management resources by station location;    -   A list of fire-management resources (such as water-tenders and        air-tankers) by their resource dependencies;    -   A list of fire-management resources with cumulative line        production quantity by time period for each fire; and    -   A list of stations with station capacities and expansion        penalties.        In addition, said method and system employ data processing in a        computer:    -   To analyze a strategic utility/benefit metric, weighted acres        managed (WAM, defined mathematically as the weighted sum of the        acres managed for all fire events as a result of optimal        resource deployment at a given budget), under different planning        scenarios involving user-selection of stations, their        capacities, and resources there-in; and    -   To generate, in a machine-readable data format, a        utility/benefit optimization model of overall strategic        utility/benefit under the different planning scenarios; and    -   To solve a stochastic integer program of a utility/benefit        optimization model by solving its deterministic equivalent using        a 2-phase optimization approach.        Said method and system then produce as output, in a machine        readable data format:    -   A list of fires with their ID, corresponding contained/escaped        status, containment time period, deployed resources, and        expected utility;    -   A list of deployed resources by kind, category, type and station        location; and    -   A distribution of the optimal utility function values, weighted        acres managed (WAM), by each scenario.

In some embodiments, it may be beneficial to calculate the list of validdisaster management resources for each fire event:

-   -   based on the arrival time of each resource relative to the        fire-event location and the containment time horizon for each        fire and/or    -   based on the nature of the workload for each fire event and the        available deployable resources during the containment horizon        for each fire.

In some embodiments, the Phase-1 of the 2-Phase optimization approachincludes a decomposition crash heuristic and/or the Phase-2 of the2-Phase optimization approach may include solving the mixed-integerprogramming model by hot-starting the model with the solution obtainedin Phase-1 of the 2-Phase optimization approach.

In some embodiments, lists of valid resources for each fire may becalculated based on lengths of containment horizons for each fire eventand available after-arrival time windows for deployed resource and/orbased on the inter-resource dependencies of deployable resources.

In some embodiments, the occurrence probability for each fire-scenariomay be calculated from historical data.

Examples of advantages of using the present invention instead ofalternative solutions include:

-   -   The model produces robust optimal decisions in the face of        uncertainty; and    -   The solution approach for the resulting very large scale        optimization model instances is time and memory effective, and        it scales well with the problem instance size.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, aspects and advantages will be betterunderstood from the following detailed description of a preferredembodiment of the invention with reference to the drawings, in which:

FIG. 1 is a representation of the business problem addressed by thepresent invention.

FIG. 2 is a representation of two-stage stochastic integer programmingmodeling used to solve a strategic budgeting problem using a two-phasedecomposition approach according to the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS OF THE INVENTION

Referring now to the drawings, and more particularly to FIG. 1, there isshown scenarios 10 comprised of fire groups 20, each of which is in turncomprised of simultaneously occurring representative fires 30. Alsoshown are resources 40 which can be assigned to only one of thesimultaneous fires, resulting in competition among simultaneous firesfor available resources.

Referring now to FIG. 2, there is shown a two-phase optimization problem200 which receives optimization input 100 on which is performed a phaseone 210 decomposition using an off-the-shelf problem solver 300 toproduce a deployment solution 230, which optimally deploys resources tothe fires to discover their resource preferences, and a phase two 250global problem optimization, which uses said off-the-shelf problemsolver 300 to solve the global problem and employs the deploymentpreference decisions made in phase one to analyze and come up with anoptimization output 400 including the optimal initial response resourceorganization.

The optimization input 100 of FIG. 2 may contain a set of input valuesrequired to solve the model. Most notably it may contain data pertainingto:

-   -   1. Fires    -   2. Fire Groups    -   3. Fire-fighting Resources    -   4. Costs        Data for each representative fire may contain its perimeter,        size (in acres), weight (fire importance, e.g., fires occurring        close to urban population have higher weights than those        occurring in remote jungles). The optimization input 100 may        also contain data pertaining to mop-up cost. A set of        simultaneous fires may be grouped together to form a fire group,        imposing additional restrictions on deployment of resources and        containment of the fires.

Resources may contain deployment and cost data pertaining to each firethey may be deployed on. Each deployable resource on a fire may containfixed cost (i.e., one time annual cost for procurement of resource),line production capacity (i.e., the capacity of the resource to containa fire by producing a line using the retardant or land cleanup tocontribute to fire containment), hourly cost (i.e., the hazard andovertime pay to the resources—machines and human crew over thedeployment period). Various other cost and capacity restrictions may bedefined in the input data, e.g., leadership, station and equipmentpenalty groups that contribute to the total cost.

In order to tackle the business problem, the present invention may allowfor the development of a robust optimization engine for analyzingcomplex fire management scenarios very quickly with fewer computationalresources in order to provide optimal strategic budgeting decisions. Thepresent invention may address a two-phase optimization problem 200 usinga phase one 210 decomposition as part of a two-phase decompositionapproach to dissociate the complexity arising from low-level deploymentdecisions from the global optimal resource organization. Inherentcomplexity of the problem may arise from the low-level deploymentdecisions associated with solving the global model. The deploymentdecisions may contribute to only approximately 10% of the total cost butapproximately 90% of the complexity. Such deployment problems may bedissociated from the global model and may be broken down into a set ofsmaller sub-problems which may then be tackled. These problems, althoughstill complex, may be relatively small and hence may be solved morequickly.

The deployment solution 230 resulting from the solution of theabove-mentioned deployment problem may optimally deploy resources to thefires to discover their resource preferences. These deployment decisionsmay then form the basis for solving phase two 250 of the problem. Oncethe global problem is set up using the deployment decisions made inphase one 210, the global problem may present additional challenges dueto its tremendous size. An average-sized global model of this typetypically has more than 1 million 0/1 variables. A model of this sizefalls into the category of Very Large Scale Optimization Problem and assuch constitutes a “very hard” problem to solve. But the global model ismade tractable as a result of the fact that underlying complexity hasbeen tackled upfront in phase one 210. As a result, the global model maybe effectively solved in a reasonable time, so that the global model nowproduces an optimal resource organization that maximizes the weightedacres managed (protected) against the wild land fires under givenbusiness and cost constraints. Such a solution meets the functionalrequirements put forth in the business problem and meets and/or exceedsthe non-functional requirements in terms of performance and software andhardware requirements.

An off-the-shelf problem solver 300 is a tool for solving linearoptimization problems, commonly referred to as linear programmingproblems. An off-the-shelf problem solver 300 may also solve a varietyof other problems including network flow problems, quadratic programmingproblems, constrained optimization problems, and so forth. Theoptimization output 400 represents the solution to the business problem.The solution may comprise of a set of representative resources (airtankers, dozers, crews, helicopters, smoke jumpers etc) that may bedeployed to the representative fires to successfully contain them. Also,the solution may contain details about the costs associated withprocurement and deployment of resources and any additional costs ofcontaining the fire (e.g.: perimeter mop-up, penalties). The model maybe solved iteratively for incrementally higher budget levels to get afrontier that facilitates cost-benefit analysis, cost being the budgetand benefit being the weighted acres managed. This may be submitted tothe budgeting and planning office for a decision on budget allocationfor the relevant fiscal year. This model may be used by the followingagencies for strategic budgeting:

-   -   1. BLM—Bureau of Land Management    -   2. NPS—National Park Services    -   3. FS—Forest Service    -   4. BIA—Bureau of Indian Affairs    -   5. USFS—US Fish and Wildlife Services

In order to solve the business problem at hand within the software,hardware and performance constraints, the proposed innovation allows thedevelopment of a robust optimization engine for analyzing complex firemanagement scenarios very quickly with fewer computational resources inorder to provide optimal strategic budgeting decisions.

In order to handle multiple scenarios corresponding to variable fireseason (one year) the problem has been modeled as a two-stage stochasticinteger programming model:

-   -   Stage 1: Resource Aguisition Problem        -   For an effective and optimal resource organization,            efficient and re-usable resources need to be acquired that            can be deployed on multiple fires. This is handled in stage            1 of the stochastic integer programming model. The resource            selection is based on their cost versus their effectiveness.    -   Stage 2: Resource Deployment Problem        -   With the efficient resource acquisition made in Stage 1,            Stage 2 optimally deploys the resources to each of the            fires.            The solution approach used to solve the above problem is a            two-phase decomposition approach:    -   Phase 1 (Decomposition): Optimal Deployment of Resources        -   This phase handles the low level complex decisions            associated with deployment of resources to each of the fires            in fire groups. The sub-model instances although complex are            small in size and can be optimized quickly to discover the            resource preference for each of the fires.    -   Phase 2: Solve Global Problem        -   This phase solves the global problem of creating an optimal            resource organization to maximize the weighed acres managed            this phase uses the deployment decision made in Phase 1. The            optimization model instance in this phase is very large but            simple to solve, as the complexity arising from the            deployment decision has been solved in Phase 1.            This two-phase decomposition approach results in a robust            optimization model that meets the functional and            non-functional requirements and solves the model within s/w,            h/w and performance constraints.

In the preferred embodiments, the two-stage stochastic integerprogramming modeling of the problem of strategic budgeting for wildfiresuses scenario-based stochastic modeling. There is a two-stage integerprogramming model in which stage one is a resource acquisition problemand stage two is a resource deployment problem. The decompositionapproach employed to solve the two-phase optimization problem involves aphase one (decomposition), which optimally deploys resources to thefires to discover their resource preferences, and a phase two, solvesthe global problem and uses the deployment preference decisions made inphase one to analyze and come up with the optimal initial responseresource organization.

While the invention has been described in terms of its preferredembodiments, those skilled in the art will recognize that the inventioncan be practiced with modification within the spirit and scope of theappended claims.

1. A computer-implemented, stochastic-integer-programming-basedconstrained optimization method to develop a strategic budget forallocation of disaster management resources to disaster events belongingto scenarios associated with occurrence probabilities comprising thesteps of: providing as input, in a machine-readable data format, a listof fire scenarios with unique IDs for each fire planning unit, and theiroccurrence probabilities; providing as input, in a machine-readable dataformat, a list of fire-groups with unique IDs including simultaneousfires in each scenario for the fire planning unit; providing as input,in a machine-readable data format, a list of fire events with unique IDsin each fire-group by one or more of fire management unit location, FireIntensity Level, and sensitivity time period; providing as input, in amachine-readable data format, a list of fire events by one or more oftheir respective weights (relative utility in the utility function),burned area cumulative perimeter growth by time period, and burned areacumulative acres growth by time period; providing as input, in amachine-readable data format, a list of fire events with valid list offire-management resources; providing as input, in a machine-readabledata format, a list of fire-management resources by one or more of kind,category and type; providing as input, in a machine-readable dataformat, a list of fire-management resources by station location;providing as input, in a machine-readable data format, a list offire-management resources (such as water-tenders and air-tankers) bytheir resource dependencies; providing as input, in a machine-readabledata format, a list of fire-management resources with cumulative lineproduction quantity by time period for each fire; providing as input, ina machine-readable data format, a list of stations with stationcapacities and expansion penalties; employing data processing in acomputer to analyze strategic utility/benefit (weighted acres managed)under different planning scenarios involving one or more ofuser-selection of stations, their capacities, and resources there-in;and employing data processing in a computer to generate, in amachine-readable data format, a utility/benefit optimization model ofoverall strategic utility/benefit under one or more different planningscenarios; employing data processing in a computer to solve a stochasticinteger program of a utility/benefit optimization model by solving itsdeterministic equivalent using a two-phase optimization approach;producing as output, in a machine-readable data format, a list of fireswith their ID, corresponding contained/escaped status, containment timeperiod, deployed resources, and expected utility; producing as output,in a machine-readable data format, a list of deployed resources by oneor more of kind, category, type and station location; producing asoutput, in a machine-readable data format, a distribution of the optimalutility function values, weighted acres managed (WAM), by each scenario.2. The stochastic integer programming based constrained optimizationmethod recited in claim 1 wherein the list of valid disaster managementresources for each fire event is calculated based on the arrival time ofeach resource relative to the fire-event location and the containmenttime horizon for each fire.
 3. The stochastic integer programming basedconstrained optimization method recited in claim 1 wherein the list ofvalid disaster management resources for each fire event is calculatedbased on the nature of the workload for each fire event and theavailable deployable resources during the containment horizon for eachfire.
 4. The stochastic integer programming based constrainedoptimization method recited in claim 1 wherein the phase one of thetwo-phase optimization approach includes a decomposition crashheuristic.
 5. The stochastic integer programming based constrainedoptimization method recited in claim 1 wherein the phase two of thetwo-phase optimization approach includes solving the mixed-integerprogramming model by hot-starting the model with the solution obtainedin phase one of the two-phase optimization approach.
 6. The stochasticinteger programming based constrained optimization method recited inclaim 2 wherein the lists of valid resources for each fire is calculatedbased on lengths of containment horizons for each fire event andavailable after-arrival time windows for deployed resource.
 7. Thestochastic integer programming based constrained optimization methodrecited in claim 3 wherein the lists of valid resources for each fire iscalculated based on the inter-resource dependencies of deployableresources.
 8. The stochastic-integer-programming-based constrainedoptimization method recited in claim 1 wherein the occurrenceprobability for each fire-scenario is calculated from historical data.9. A system employing stochastic-integer-programming-based constrainedoptimization technology for developing a strategic budget for allocationof disaster management resources to disaster events belonging toscenarios associated with occurrence probabilities comprising: means forproviding as input, in a machine-readable data format, a list of firescenarios with unique IDs for each fire planning unit, and theiroccurrence probabilities; means for providing as input, in amachine-readable data format, a list of fire-groups with unique IDsincluding simultaneous fires in each scenario for the fire planningunit; means for providing as input, in a machine-readable data format, alist of fire events with unique IDs in each fire-group by one or more offire management unit location, fire intensity level, and sensitivitytime period; means for providing as input, in a machine-readable dataformat, a list of fire events by one or more of their respective weights(relative utility in the utility function), burned area cumulativeperimeter growth by time period, and burned area cumulative acres growthby time period; means for providing as input, in a machine-readable dataformat, a list of fire events with valid list of fire-managementresources; means for providing as input, in a machine-readable dataformat, a list of fire-management resources by one or more of kind,category and type; means for providing as input, in a machine-readabledata format, a list of fire-management resources by station location;means for providing as input, in a machine-readable data format, a listof fire-management resources (such as water-tenders and air-tankers) bytheir resource dependencies; means for providing as input, in amachine-readable data format, a list of fire-management resources withcumulative line production quantity by time period for each fire; meansfor providing as input, in a machine-readable data format, a list ofstations with station capacities and expansion penalties; means foremploying data processing in a computer to analyze strategicutility/benefit (weighted acres managed) under different planningscenarios involving one or more of user-selection of stations, theircapacities, and resources there-in; and means for employing dataprocessing in a computer to generate, in a machine-readable data format,a utility/benefit optimization model of overall strategicutility/benefit under one or more different planning scenarios; meansfor employing data processing in a computer to solve a stochasticinteger program of a utility/benefit optimization model by solving itsdeterministic equivalent using a two-phase optimization approach; meansfor producing as output, in a machine-readable data format, a list offires with their ID, corresponding contained/escaped status, containmenttime period, deployed resources, and expected utility; means forproducing as output, in a machine-readable data format, a list ofdeployed resources by one or more of kind, category, type and stationlocation; means for producing as output, in a machine-readable dataformat, a distribution of the optimal utility function values, weightedacres managed (WAM), by each scenario.
 10. The stochastic integerprogramming based constrained optimization method recited in claim 1wherein the list of valid disaster management resources for each fireevent is calculated based on the arrival time of each resource relativeto the fire-event location and the containment time horizon for eachfire.
 11. The stochastic integer programming based constrainedoptimization method recited in claim 1 wherein the list of validdisaster management resources for each fire event is calculated based onthe nature of the workload for each fire event and the availabledeployable resources during the containment horizon for each fire. 12.The stochastic integer programming based constrained optimization methodrecited in claim 1 wherein the phase one of the two-phase optimizationapproach includes a decomposition crash heuristic.
 13. The stochasticinteger programming based constrained optimization method recited inclaim 1 wherein the phase two of the two-phase optimization approachincludes solving the mixed-integer programming model by hot-starting themodel with the solution obtained in phase one of the two-phaseoptimization approach.
 14. The stochastic integer programming basedconstrained optimization method recited in claim 2 wherein the lists ofvalid resources for each fire is calculated based on lengths ofcontainment horizons for each fire event and available after-arrivaltime windows for deployed resource.
 15. The stochastic integerprogramming based constrained optimization method recited in claim 3wherein the lists of valid resources for each fire is calculated basedon the inter-resource dependencies of deployable resources.
 16. Thestochastic integer programming based constrained optimization methodrecited in claim 1 wherein the occurrence probability for eachfire-scenario is calculated from historical data.
 17. Acomputer-implemented method for predicting or optimizing the budgetneeded for allocation of disaster management resources to a plurality ofdisaster events, comprising the steps of: providing input to a computer,in a machine-readable data format, information (I) describing attributesof a plurality of available disaster management resources, (II)describing a plurality of disaster scenarios; and performing a two-phasestochastic optimization on said input wherein a first phase of saidtwo-phase optimization produces a deployment solution which identifiesresource preferences for particular disasters of said plurality ofdisasters, and wherein a second phase of said two-phase optimizationidentifies which resource of said one or more available disasterresources is assigned to a particular disaster scenario based on theresource preferences identified in the first phase.
 18. Thecomputer-implemented method recited in claim 17, wherein phase one ofthe two-phase stochastic optimization is a decomposition.
 19. Thecomputer-implemented method recited in claim 17, wherein phase two ofthe two-phase stochastic optimization is a global problem optimization.